How Long to Read Quasi-Linear Perturbations of Hamiltonian Klein-Gordon Equations on Spheres

How Long Does it Take to Read Quasi-Linear Perturbations of Hamiltonian Klein-Gordon Equations on Spheres?

It takes the average reader 1 hour and 20 minutes to read Quasi-Linear Perturbations of Hamiltonian Klein-Gordon Equations on Spheres by J.-M. Delort

Assuming a reading speed of 250 words per minute. Learn more

Description

The Hamiltonian ∫X(∣∂tu∣2+∣∇u∣2+m2∣u∣2)dx, defined on functions on R×X, where X is a compact manifold, has critical points which are solutions of the linear Klein-Gordon equation. The author considers perturbations of this Hamiltonian, given by polynomial expressions depending on first order derivatives of u. The associated PDE is then a quasi-linear Klein-Gordon equation. The author shows that, when X is the sphere, and when the mass parameter m is outside an exceptional subset of zero measure, smooth Cauchy data of small size ϵ give rise to almost global solutions, i.e. solutions defined on a time interval of length cNϵ−N for any N. Previous results were limited either to the semi-linear case (when the perturbation of the Hamiltonian depends only on u) or to the one dimensional problem. The proof is based on a quasi-linear version of the Birkhoff normal forms method, relying on convenient generalizations of para-differential calculus.

How long is Quasi-Linear Perturbations of Hamiltonian Klein-Gordon Equations on Spheres?

Quasi-Linear Perturbations of Hamiltonian Klein-Gordon Equations on Spheres by J.-M. Delort is 80 pages long, and a total of 20,000 words.

This makes it 27% the length of the average book. It also has 24% more words than the average book.

How Long Does it Take to Read Quasi-Linear Perturbations of Hamiltonian Klein-Gordon Equations on Spheres Aloud?

The average oral reading speed is 183 words per minute. This means it takes 1 hour and 49 minutes to read Quasi-Linear Perturbations of Hamiltonian Klein-Gordon Equations on Spheres aloud.

What Reading Level is Quasi-Linear Perturbations of Hamiltonian Klein-Gordon Equations on Spheres?

Quasi-Linear Perturbations of Hamiltonian Klein-Gordon Equations on Spheres is suitable for students ages 10 and up.

Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.

When deciding what to show young students always use your best judgement and consult a professional.

Where Can I Buy Quasi-Linear Perturbations of Hamiltonian Klein-Gordon Equations on Spheres?

Quasi-Linear Perturbations of Hamiltonian Klein-Gordon Equations on Spheres by J.-M. Delort is sold by several retailers and bookshops. However, Read Time works with Amazon to provide an easier way to purchase books.

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